Why don't we connect the flyback diode between two ends of inductor instead of between one end and ground in the figure below?

 

What ?? Where is a ground in your digram?

 

What ?? Where is a ground in your digram?

With ground I meant "negative pole" of the battery.
Why not connect anode of the diode to the other end of inductor?

 

Well, I misunderstood here. The diode is not flyback diode.

 

Why not connect anode of the diode to the other end of inductor?

Such a connection will waste the energy stored in coil to "heat" the diode.
In a buck converter some energy is transferred directly from the source to the load, and during Toff time the coil drives the load.
https://en.wikipedia.org/wiki/Buck_converter#/media/File:Buck_operating.svg

 

Yes, I see. With that connection, during Toff the loop formed by inductor and diode and no energy is transferred to load.

 

Well, I misunderstood here. The diode is not flyback diode.

I think the diode is still called flyback diode?

 

Yes, but the catch diode, and freewheeling diode are also in use.